A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.50$, and bags of cookies cost $$2.50$, and sales equaled $$42.00$ in total. There were $6$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Answer: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6.5x+2.5y = 42}$ ${y = x+6}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+6}$ for $y$ in the first equation. ${6.5x + 2.5}{(x+6)}{= 42}$ Simplify and solve for $x$ $ 6.5x+2.5x + 15 = 42 $ $ 9x+15 = 42 $ $ 9x = 27 $ $ x = \dfrac{27}{9} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+6}$ to find $y$ ${y = }{(3)}{ + 6}$ ${y = 9}$ You can also plug ${x = 3}$ into $ {6.5x+2.5y = 42}$ and get the same answer for $y$ ${6.5}{(3)}{ + 2.5y = 42}$ ${y = 9}$ $3$ bags of candy and $9$ bags of cookies were sold.